Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...

This paper brings together Dana Scott’s measure-based semantics for the propositional modal logic S4, and recent work in Dynamic Topological Logic. In a series of recent talks, Scott showed that the language of S4 can be interpreted in the Lebesgue measure algebra, M, or algebra of Borel subsets of the real interval, [0, 1], modulo sets of measure zero. Conjunctions, disjunctions and negations ...

Let A be a partial *-algebra endowed with a topology that makes it into a locally convex topological vector space AA]. Then A is called a topological partial *-algebra if it satisses a number of conditions, which all amount to require that the topology ts with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of...

Using a formalism of minitwistors, we derive infinitely many conserved charges for the sl(∞)-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions. E-mail address; be10@dk...

The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced.We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, ...

We study the hamiltonian reduction of affine Lie superalgebra sl(2|1)(1). Based on a scalar Lax operator formalism, we derive the free field realization of the classical topological topological algebra which appears in the c ≤ 1 non-critical strings. In the quantum case, we analyze the BRST cohomology to get the quantum free field expression of the algebra.

The paper proposes the notions of topological platform and quantalic topological theory for the presentation and investigation of categories of interest beyond the realm of algebra. These notions are nevertheless grounded in algebra, through the notions of monad and distributive law. The paper shows how they entail previously proposed concepts with similar goals.

To any germ X of a complex analytic variety with local ring OX one associates the topological Lie algebra Θ(X) = DerOX of vector fields on X. We show that isolated hypersurface singularities X of dimension at least 3 are uniquely determined up to isomorphism by the topological Lie algebra Θ(X).

Let (A,Ao) be a topological quasi *-algebra, which means in particular that Ao is a topological *-algebra, dense in A. Let πo be a *-representation of Ao in some pre-Hilbert space D ⊂ H. Then we present several ways of extending πo, by closure, to some larger quasi *-algebra contained in A, either by Hilbert space operators, or by sesquilinear forms on D. Explicit examples are discussed, both a...